Babylonian religion is known from clay, and clay preserves what was written down rather than what was believed. The distinction matters more here than almost anywhere else.
The great literary texts, Enuma Elish and the Epic of Gilgamesh among them, survive in multiple recensions across many centuries and many sites, so it is possible to watch them change. That is a rare advantage. It is also a warning, because a version copied for a particular temple in a particular reign is a version with an interest.
Alongside the literature sits an enormous administrative and ritual archive: offering lists, temple accounts, god lists that catalogue deities and equate them with one another, omen series, incantations and prayers. The god lists in particular are the reason so much can be said about the structure of the pantheon. They are scholarly compilations, produced by scribes who were themselves systematising a religion that had grown by accretion, and they should be read as such rather than as neutral inventories.
What is thin is ordinary practice. The archives belong to temples and palaces, and the religion of a household is visible mostly through amulets, figurines and the incantations used against illness and bad luck. A great deal of what an ordinary Babylonian did about the divine is inferred rather than read.
Decipherment also shapes what is visible. Akkadian was recovered in the nineteenth century, and the corpus is still being edited and published, so the picture continues to move.